# Convergence of the Iterates for Momentum and RMSProp for Local Smooth Functions: Adaptation is the Key

arXiv: https://arxiv.org/abs/2407.15471 · HTML: https://mlsanity.com/paper/2407.15471/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2024.

## Built on by (most cited first, 2 of 2)

- [WTNN: Weibull-Tailored Neural Networks for survival analysis](https://mlsanity.com/paper/2512.09163/) (2025)
- [Convergence rates for the RMSprop optimizer with full control of the hyperparameters](https://mlsanity.com/paper/2608.30382/) (2026)

## Abstract (arXiv)

Both accelerated and adaptive gradient methods are among state of the art algorithms to train neural networks. The tuning of hyperparameters is needed to make them work efficiently. For classical gradient descent, a general and efficient way to adapt hyperparameters is the Armijo backtracking. The goal of this work is to generalize the Armijo linesearch to Momentum and RMSProp, two popular optimizers of this family, by means of stability theory of dynamical systems. We establish convergence results, under the Lojasiewicz assumption, for these strategies. As a direct result, we obtain the first guarantee on the convergence of the iterates for RMSProp, in the non-convex setting without the classical bounded assumptions.